INFORMAL XII. 1, Winter 1990

In the Service of Human Society: Formal, Informal or Anti-Logical? The of the Logician Evert Willem Beth (1908-1964)

E. M. BARTH Groningen University

Introduction 1. Where does European argumentation theory come from? Proof as a social act The topic on which I have been asked to speak is, as far as I understood it, the Where does the highly amorphous field formal-informal divide in logic. Having called argumentation theory derive from? pondered about that task for a long time I There is, I believe, a certain difference be­ decided that concerning a weighing of the tween the United States on the one hand and pro's and con's of the two approaches I Europe and Canada on the other in this want to cut it short and to simply say: respect. Whereas in the United States the There ought to be formal logic, attuned departments of speech communication seem to human affairs; to have been very influential indeed, in There ought to be informal logic, attuned Europe argumentation theory derives from to human affairs; philosophy, and to a very large extent from logic-as in Canada. and once upon a time the twain shall meet. This fact is of considerable importance I do not accept the formal-informal for an understanding of the possibilities of, divide as a divide. That distinction ought and in, the field, as I shall try to show. Five to be played down. It is merely a question European philosophers at least from the of method-an interesting question, but not generation before us must be mentioned, at all a threatening one. A plurality or without whom this field would hardly have richness of methods is something to rejoice in. existed in Europe. They are, in Second, I have noticed a not unsurpris­ chronological order of the onset of their ing lack of understanding of the origins of work, Arne Naess of Norway, Chaim argumentation theory, especially in so far Perelman and Lucie Olbrechts-Tyteca of as these are European origins. I believe that Belgium, Evert Willem Beth of the a better understanding of those origins may , Paul Lorenzen of the German contribute to a lessening of tensions caus­ Federal Republic. One of the logicians in ed by the formal-informal divide. question, Arne Naess, has used informal I shall try to work on your ideas by way methods-which made the Wiener Kreis of feeding your fantasy rather than by argu­ philosophers unwilling to take his 1936 ing. I'll supply you with a case history about "discussion calculus" seriously. Beth and one human being, the Dutch logician­ Lorenzen are formal logicians. I want to philosopher Evert Willem Beth, who was show that this last difference is less impor­ born in 1908 and died in 1964. His tant than some hold it to be-much less dialogically oriented philosophy happens to important. be one of the basic sources of argumentation To start with, what these two formal theory in Europe. I shall not discuss tech­ logicians, Beth and Lorenzen, have done nical details but concentrate on his outlook is certainly not triviaL I can prove-in an on logic and the needs of humanity. I do indirect manner, by means of a couple of that, however, by means of a short detour. case histories-that it is not. In 1977 the 2 E. M. Barth

logician Yu. I. Manin published (an English that moment, in 1951, Church was editor­ version ot) his textbook on the intimidating in-chief of the Journal of Symbolic Logic subject of mathematical logic, this belov­ (the JSL). Beth was a member of its editorial ed play-pen of autistic academics (my judge­ board and had been so since shortly before ment, not his). The book contained one par­ World War II. On 11 June 1951 Beth writes ticularly remarkable section, so unusual that to the then editor-in-chief of the JSL, Alon­ a couple of years later the journal The zo Church, to tell him that he is very disap­ Mathematical Intelligencer published it. pointed in a review that Church had sent Manin's "provocative digression on him in manuscript for his information, of proof", as The Mathemtical Intelligencer his own book Fondements de Logique, writ­ called it, turns out to be the following ten in French. The review, intended for the philosophical statement: JSL, is not yet printed and Beth asks Church It A proof only becomes a proof after the to request the reviewer to revise it. is a social act of "accepting it as a proof'. This very negative review that points out a is as true for as it is for physics, number of technical inaccuracies and linguistics, or biology. The evolution of mistakes in Beth's book; and this is the on­ commonly accepted criteria for an argu­ ly aspect of the book to which the reviewer ment's being a proof is an almost untouch­ has paid any attention at all. Beth regards ed theme in the history of science. I this as extremely unfair, considering what Then the act of "proving", too, is a social he himself sees as the general aim of the act. book. He also (correctly) is of the opinion This is what the editors of the journal that a number of the mistakes or errors the The Mathematical Intelligencer found pro­ reviewer refers to hardly can be characteriz­ vocative. Manin's statement was, of course, ed as errors at all. He writes: very much in line with the spirit of the I do not question the competence of Miss dialogical form oflogic, whether formal or Novak [the reviewer]. Nor do I fail to informal. 2 recognize that, to my regret, my In the same issue of The Mathematical "Fondements" contains a number of errors. Intelligencer, the editors had invited two I feel however-and this feeling seems to be other mathematical logicians (in the nar­ shared by other reviewers-that these errors, most of them being minor slips, do not rower sense) to participate in a discussion seriously detract from the intrinsic value of about this thesis and the rest of the reprinted the book. Therefore I think that a review section. One of them was Solomon Fefer­ which restricts itself to listing some of these man from Stanford University. However, errors and adds a number of would-be in his answer to Manin, Feferman does not mistakes, cannot do justice to my book. discuss a single one of Manin's remarks. Church answers with a letter of 22 June, saying that he personally accepts the review and will publish it. He writes: 2. Logic and cultural politics I believe that the explanation must be that your book was written hastily, under If the Manin-Feferman verbal exchange pressure ofthe many other obligations that can be called a discussion, then Feferman I know you have undertaken, and that you has lost it, for he does not deal with the simply failed to take the care and make the thesis in question. I would like to compare many detailed checks which a work of this this discussion (if it is one) with one that sort demands ... .I do regret, when books of took place twenty -eight years earlier, be­ a low quality in matters of logic are being written, the necessity of publishing an un­ tween the Dutch logician-philosopher Evert favorable review of an author [Beth] of real Willem Beth3 and the American Alonzo standing in our field. But you must realize Church, of the undecidability theorem. At that this consideration has another Beth as Logician 3

side. [Certain authors of books on logic, In another letter, addressed to S. C. among which is the psychologist Piaget] may Kleene, Beth writes: deceive the outsider, but not the serious stu­ dent of modern logic. The Journal is after I am completely at a loss as to the motives all addressed primarily to logicians, and it behind Church's action or the lack of such is precisely the errors of recognized logi­ motives (italics mine). cians which it is most important to correct 'Or the lack of such motives': this seem­ if our Reviews section is to perfonn its func­ tion (italics mine). ingly fortuitous, casual remark is in my opi­ nion the pivot on which the Beth-Church In his reply of June 30, Beth starts by discussion hinges. Church was not inspired saying that he appreciates the frankness of by the goals and ideals that inspired Beth. Church's letter. This new letter of Beth's Beth looked in vain for signs of the same runs to three full typed pages. The second motivation in others, suspected a gap where half of this letter is of general logico­ he himself was a sea of fire and purposeful philosophical interest. Beth now writes: elan, and was in this respect indeed a loner among his colleagues. As these words and It seems to me that your outlook on the situa­ the discussion in which they were uttered tion as a whole is entirely mistaken and that, no less than the reviewer, [you] fail to probably make clear Beth was-like Manin, realize the fact that the book was written for though without publishing any explicit state­ French readers. Since 1940, the following ment to that-inspired by a semiotical two­ books have been published in France (here role philosophy which he very consistent­ five names of authors follow). I do not think ly put into practice. Thus one writes that my book, in spite of a number of regret­ something, or proves something, for table mistakes, is worse than any of them. someone-and that sentence form is an ir­ Nevertheless, a French reader who consults the Journal in order to decide which book reducible form. he should choose will presumably not By means of this expression 'a choose mine. For this reason, the publica­ semiotical two-role philosophy' I hope to tion of the review is unjust. Now your argu­ stimulate the readers to compare Beth's ment is that the books Lon logic] I mention­ logical and semiotical philosophy (in its en­ ed [as not well-informed] are not by tirety) with certain other trends of thought recognized logicians and therefore less harmful. But this is certainly not the opinion in and concerning logic, first with the ofprospective readers. In their opinion, the philosophy of the Dutch solipsist authors I mentioned are rccognized mathematician L. E. J. Brouwer (in its en­ specialists in logic, and this opinion will be tirety), and then with the of corroborated by the review in the JournaL more pragmatical authors such as the logi­ In this connection I cannot help remind­ cians Paul Lorenzen, Arne Naess, or Leo ing you of my letter of July 29, 1950, in Apostel, or with that of Richard Rorty. which I warned you against the repercus­ sions of your policy in France. Summing up: Church is seen to use ex- I enclose a list of corrections to my book pressions such as which I have compiled since its publication and which will be published as soon as a work of this sort possible. our field I think it will be clear that I cannot under the outsider the present circumstances remain a con­ the serious student of logic. sulting editor of the Journal. I therefore wish to submit to you my resignation, leaving it Not very shocking, but the difference with to you to decide at which date within the cur­ Beth's less usual language is impressive. In rent year you prefer to drop my name from Beth's letters we find the expressions: the cover ... (italics mine, E. M. B.). the book was written for ... readers The letter ends on an extremely polite note. the opinions of prospective readers 4 E. M. Barth

the lack of such motives tre; and that he wanted the results to be us­ a powerful expedient for rational critique ed to improve human thinking in general. philosophical and political systems I shall call this the empirical component of a great lack of command of logic, his philosophy of logic. even in intellectual circles [2] He regarded the improvement of critical thinking (notably about human thinking as one necessary condition philosophical and political systems) for the improvement of the human world­ the indispensable ingredient called of human relations, and of human activities, teaching methods verbal and non-verbal. This I shall call the pragmatical component of Beth's philosophy of logic. We could also call it 3. Logic as rational critique: the culture-oriented component. It is A culturally relevant discipline with especially this component which empirical and pragmatical components distinguishes Beth from the intuitionist mathematician L. E. J. Brouwer. 4 Evert Willem Beth was and is the [3] He assumed that 'the new logic' (so­ undisputed star of post-war work in called mathematical logic, provided that ex­ philosophical as well as mathematical logic pression is taken in its widest sense), were in the Netherlands. Among professional it to become generally known and used, logicians Beth's methods and results in would mean an important step forward in mathematical logic are famous. His work structuring human thinking: in the logical history of ideas is less well Logic now does not only serve the construc­ known-some of it has fortunately leaked tion and investigation of mathematical and out of the country, though it has by far not other deductive theories, it is moreover also made the impact it deserves. But his general a powerful expedient for rational critique. vision of the incorporation of logical pro­ The creation and continuation of all kinds blems and logical investigations into the of philosophical and political systems is only general cultural activity was so unusual that possible owing to a great lack of command of logic, even in intellectual circles. 5 neither the Dutch nor the international society of professional logicians could ab­ Beth here declares himself as not being sorb it. Beth's view on logic and its func­ an adherent of philosophical rationalism. He tion in society is clearly based on a two­ clearly was a staunch believer in both the role semiotics-see above. It can perhaps practical and the theoretical value of the in­ be characterized as follows: tellect, in daily life no less than in the [1] He realized that theories concerning sciences. However, he did not adhere to the logic, old and new, to a considerable degree basic value of rationalism, which is the idea reflect forms of cognition which are decisive that to be engaged in abstract logic and for human thought, also outside mathematics is 'the highest' cultural value mathematics. And he assumed that a world­ and therefore the only professional 'end in wide improvement of (theoretical and) prac­ itself' for mathematicians and for logicians tical logic is one necessary condition for the as well. His many and varied activities and long-tenn improvement of human thinking. his many and varied publications in fact Empirical logical-cognitive research, be it demonstrate an uncommon system of of an historical or a psychological or a values-uncommon among logicians. 6 linguistic character, will disclose the dif­ Now for the empirical component of ferences and the weaknesses of contem­ Beth's philosophy. Beth wrote a number of porary modes of practical and theoretical books and articles on the history of thought. We may quite safely say that he mathematics and of logic. 7 Many of these envisaged a 'cognitive science' avant 1a 1et- are of the encyclopedic type and reflect his Beth as Logician 5

educational zest. More important than these Lorenzen equates his own method ofdialo­ surveys is his own research into hidden gical tableaus with Beth's semantical tableaus. logical patterns and (sometimes) doctrines This is his letter, translated into English: and of how they have functioned in Western Sehr verehrter, Ueber Herr Beth, intellectual history. We shall return to this in Section 6 below. Perhaps this letter will reach you before your In order to bring about an improvement departure to Warsaw. I am looking forward to meeting you there-for I have just receiv­ in the direction of a science of logic with ed your new great book [The Foundations empirical and cultural bearings as Beth ofMathematics] and have started reading it, hoped for, it is necessary, I believe, that in great excitement. we learn to see as institutions. It is so rich in content that I have of Precisely this approach is recommended in course so far only been able to read some a recent book by the American philosopher of it, but I should like already now and John L. Pollock. 8 'For philosophical pur­ without reservation to congratulate you with it-with the mathematical elegance with poses', Pollock writes, 'the institution can which you prove all important questions as be identified with the set of its constitutive well as for the light that you throw upon rules' (p. 211). In the case oflogics the con­ philosophical-historical connections. stitutive rules comprise at least the set of Your new auxiliary, the semantical rules distributing rights and obligations over tableaus, are now very nicely and clearly ex­ the players, or, better, over the logical posed. I am particularly interested in these tableaus for another reason, too-and it roles. One may want to add also the ends would be extremely pleasant if we could for which a certain linguistic company have a close talk about it together in Warsaw. (culture) seems to have involved certain In my attempts at defining the expression argumentative uses of language, in as much definite, as I have used it in my Einfuhrung as those uses of language-rules and obliga­ in die operative Logik und Mathematik, I tions of the players in debates-can be seen have investigated how the logical constants to implement these ends. Pollock writes: are applied when they occur in a dialogue (between a Proponent, P, and an Opponent, The conception of institutions which 0). When this dialogical usage of the logical emerges from these examples is that they are constants is defined (in a rather obvious essentially moral and legal instruments of manner) and the ensuing dialogues written a certain sort, and participation consists of down, then I arrive preciseJy at your the performance of acts whereby one acquires tabJeaus (with minor differences). certain kinds of moral and legal obligations May I briefly demonstrate this in con­ with respect to the institution (p. 223). nection with your example "festino"? When applied to logic(s), this is exact- -asks Lorenzen, and sets to work. 9 ly the insight that is needed for the purpose of constructing a technical normative logic which can be used clinically as well as 5. The theoretical side of the pragmatical constructively-as intended by Beth. component of Beth's thought: his work as an organizer of the world of logic

4. The relation of Beth's work to the logic This belongs so to speak to the of dialogue and dialogical formal logic theoretical side of the pragmatical compo­ nent in Beth's thinking. That pragmatical A letter from Lorenzen to Beth, writ­ component also had a practical side to it. ten 17 August 1959, offers a particularly Beth put a remarkable amount of energy and poignant though indirect demonstration of time into the construction or reconstruction that two-role semiotics upon which Beth's of national and international associations for own philosophy is based. In this letter logic and the philosophy of science. Mr. P. 6 E. M. Barth van Ulsen who has set up the Beth archives Mathematics, 1935) came a number of in Amsterdam writes: books that discussed the philosophy of mathematics from a systematic point of Beth wanted to have a special organization for the philosophy of science and logic, in­ view, as well as books on the philosophy dependent from the ICHS, the International and the history of mathematics (1944), the Council of Humanistic Science (in which history of logic (1942, 1944), on symbolic one would have to deal with philosophers logic itself (1950), and on the philosophy in general, who might very well want to par­ of space (1959). In 1942 he published an ticipate in decision making on topics they unorthodox analysis of Kant's classification could not possibly understand). Neither did of judgements into analytical and synthetical he want it to become a sub-department of the IMU, the International Mathematical (cf. Beth 1953). Union; for he feared that the mathematicians Whereas some of his papers may be might drop the logicians and the classified as a contribution to the history of philosophers of science, as a consequence theoretical semantics, other ones are bet­ of their lack of affinity to these fields .10 ter characterized as belonging to the history of concealed but extremely influential assumptions with a logical impact. This lat­ 6. The foundations of factual systems of ter field is the intersection of what is now thought: "Knowledge representation" called knowledge representation and em­ and empirical logicll pirical logic. In Beth's work one finds three such themes: (1) his analysis of the history, Bordering on mathematical activities on philosophy and systematical surroundings the one side and on historico-philosophical of the so-called method of exposition con­ activities on the other there is a field of cerning Aristotelian syllogistics; (2) of the research that has as yet attracted but few Platonic-Aristotelian cognitive Principle of practitioners. Beth was the first Dutch logi­ the Absolute; (3) of the Postulate of Self­ cian to work in this field, but he had a Evidence (' 'het evidentiepostulaat' '). number of well-known predecessors­ For reasons of time and space I shall not , Leonard Nelson, and here have the opportunity to discuss the others. Still other names are Magdalena methodological problems and the results of Aebi, Arthur Prior, laakko Hintikka, the this type of analysis. present author, and Philip Kitcher. This is Beth did not restrict his philosophical the investigation of the various logical and and dialogical perspective to Western seman tical assumptions and paradigms that thought12 (not to mention the possibility of dominate or that have dominated human restricting it to Europe): minds, in fact rather than ideally, and which therefore determine in no small degree the For a philosophical study of logic ... a fur­ scientific as well as the political systems ther knowledge of the logic of non-Western cultures can be of importance, Beth wrote wrought by man. These assumptions can be, in 1960 ... .In the first place we shall have but need not have been, openly formulated to pay attention to the availability of as the doctrines of some normative logic; equivalents of our current means of expres­ sometimes they are. sion for negation, implication (if ... then), Beth came to this task well prepared, generalization, and the modalities, and of having already undertaken numerous in­ seman tical concepts such as true and false. vestigations into the history of mathematics In addition one has to count with the possibility that in connection with formal and the history of philosophy, and into the reasoning, and perhaps also in descriptions history of logic in particular. After his doc­ of formal reasoning, an appeal is made to toral thesis, Rede en aanschouwing in de other logical and semantical concepts than wiskunde (Reason and Intuition in those that are current here and now. 13 Beth as Logician 7

Given his cultural ideals and After Beth's death the outlook that logic philosophical values, Beth may be said to also has a task as a guide for critical think­ have made a serious strategic mistake in put­ ing is as a rule (there are exceptions) not ting those pages together with more than taken seriously by Dutch logicians, no more five hundred pages on the foundations of than by logicians in other countries. IS mathematics (as that field appeared to him Academic fashion and philosophical ra­ in 1959), in one huge volume with this for­ tionalism prevails above common sense, in bidding title, rather than publishing these the Netherlands as everywhere. Beth, eighty or so pages separately under another however, wrote: name so that it would seem accessible to Now, by this development, fonnallogic has the general philosopher. The title, Founda­ not in the least lost its suitability for critical tions ofMathematics, seems to keep every thinking; the contrary is true. However, in philosopher who is not highly skilled in the way of exposition of formal logic com­ abstract mathematics away from those mon at present, the subjects which would eighty pages as well, to the serious detri­ deserve attention with respect to this objec­ ment of the now budding field of tive come to lie far apart. Therefore one can­ "knowledge representation". not get to know these subjects without im­ mersing oneself in all kinds of problems which are exclusively important for those who study logic for its own sake, or for the 7. Differing motives behind preoccupation sake of mathematical foundational studies. with logic; Beth on critical thinking This means, Beth thinks, that we are con­ fronted with the problem of restructuring On this topic Beth writes, in the in- the teaching of logic in such a way that troduction to his Aspects ofModem Logic: logic-formal logic-can fulfill this ex­ In the practice of formal logic there have tremely important cultural task of serving always been three guiding motives: as a directive for critical thinking: - interest for the problems oflogic as such, the clarification of the inner relationship In my opinion, this is mostly to be blamed of certain deductive disciplines (usually on a lack of the indispensalbe ingredient call­ mathematical theories), ed teaching methods. Take the numerous in­ - and the need for a directive for critical troductory books which have appeared in the thinking (notably about philosophical and last years. With all their good intentions, political systems). none of the them succeed in imparting to the In the last decades fonnal logic has also turn­ reader what he really needs ... 16 ed out to be important for the thcory of I shall not delve into Beth's own sugges­ digital computers; otherwise the emphasis, however, falls on the first two motives, tions for the teaching oflogic here. It seems which is, alas, detrimental to the applica­ more important to emphasize that formal tion of formal logic as a guide for critical logic still does not fulfill the educational thinking. This [unfortunate fact] is related functions Beth considered it to potentially to the bonds of modem formal logic, have. It looks as if in this world no more abstract mathematics and mathematical func­ than two ideals, or two attitudes, inform the tional studies, and to the specialistic minds of the majority of professional character which symbolic logic has conse­ logicians-a semi-religious belief in Reason quently more and more obtained. 14 as the one and only Ultimate Value, and in As to clarity this leaves nothing to be professional logicians or mathematicians as desired. Notice the objectives he himself at­ its blessed prophets; or else, unadulterated tributes to "critical thinking": he mentions careerism. A combination ofthe two is not philosophical systems and political systems infrequent. as well. Beth was exceptional in this respect. He 8 E. M. Barth

took an enormous personal joy in human being whosoever may form a really mathematical theories and new theses, and homogeneous unit, Beth's mind may be said he had a clear ambition and desire for to have been so to a degree that was com­ recognition. But in addition to this he had pletely unusual among his professional col­ other ideals as well, and he fought for them leagues all over the world. in all directions, never claiming anyone Concerning the formal-informal divide aspect of human logic to be the absolute and Beth wrote, in 1961: exclusive one, never condescending toward any field of human logic, provided it made Formal and informal logic, the formalized some distinction between good and bad languages, and the specialized technical languages of human communication do not rules of reason or argumentY appear simply as separate and independent Precisely what moved Beth? What spur­ occupations: they complete each other and red him on? It is difficult to put oneself in­ influence one another. IS to anyone else's mental position, and it is dangerous to think that one can. And yet It is fascinating, though saddening, to watch I will try. how people who personally have an entirely Beth was-and remained throughout his negative or zero relation with (modern) whole life-extraordinarily preoccupied logic again and again unite academically with the terrors of World War II and its with those logicians and mathematicians cultural roots, the rise and effects of fascism who wish to restrict the very definition of and other totalitarian modes of thought. He logic to algebraic methods and the founda­ did not, as is usual, relegate his reactions tions of mathematics, which they then serve to them to a secluded part of his brain that up to the students in other departments in was closed off from his professional work, diluted form. 19 With the blessing and en­ or vice-versa. Though the mind of no couragement of the logic-haters.

Notes

I The Mathematical Intelligencer, vol. 2. no. 1. the articles in NCR Handelsblad by Rudy See also: Yu. 1. Manin. A Course of Kousbroek, October-November 1982. This Mathematical Logic. Springer-Verlag, 1977. book of Brouwer's has never been translated-a (Empirical logic as a logical discipline is intend­ remarkable but understandable fact, since the ed to take up, among other things, precisely this book discloses an inhumanity of the most development of criteria for the goodness or serious kind (total disregard for other people's badness of arguments-though not as restricted well-being and even for their lives: combined to mathematics). with contempt for language and logic as means for communication). 2 Manin goes on to speak about "levels ofproof­ ness", saying that 'Every proof that is written 5 Beth (1970). p. 74. Professor S. 1. Doorman must be approved and accepted by other reminded me of this passage. mathematicians, sometimes by several genera­ tions of mathematicians' (Lc.). Cf. E. C. W. 6 The quotation from Peirce in Beth's famous Krabbe's "levels of strictness" in , paper 'Semantic Entailment and Formal in 'A Theory of Modal Dialectics', fournal of Derivability' (Mededelingen der Kon. Akad. Philosophical Logic 15 (1986), 191-217. van Wet.. N. R., vol. 18, No. 13, Amsterdam: North Holland, 1955) seemed to one reader 3 Beth is probably best known as the father of (who told me so) to testity to the same purely the method of semantic tableaux, and also of rationalist pattern of values in Beth's mind as a theorem in the theory of definition. Opus in the minds of other logicians of his time. This magnum: Beth (1959). is a complete misunderstanding. Given impor­ 4 See L. E. 1. Brouwer. Leven. kunst en mystiek tant parts of his (1959) and the collection of (Life, Art, and Mysticism), Delft: 1905; also philosophical papers (1968), and the drift and Beth as Logician 9

direction of his organizational endeavors, what 14 Lay-out by the present author. we have said about him stands unrefuted by this one quotation. We shall have to grant a thinker 15 Except, of course, in my own department! who is trained in mathematics an occasional 16 Cf. Beth (1970), p. 78; the quotation is from reference to the delights of mental work! the Dutch original (p. 78) as translated by me; emphases are also mine. E. M. B. 7 SeeJ. F. Staal's bibliography of Beth's works (1965). 17 Some years ago the professorial chair that once was erected for Beth was taken off the payroll 8 John L. Pollock, Language and Thought of the Faculty of Philosophy of the University Princeton, N.J.: Princeton U.P. 1982. The of Amsterdam and moved to that of philosophy offered in this book tallies very well Mathematics. Since then the once world famous indeed with Beth's and Manin's. Institute for Logic and the Foundations of the Exaet Sciences belongs to the past-precisely 9 See here also my 'Logic to some purpose­ Ten theses against the Deductive-Nomological what Beth during his last illness feared might Paradigm in the science of logic', in: Argumen­ happen. It is not likely that that university will tation: Across the Lines of Discipline. Pro­ provide a chair for Logic from which his ideal ceedings of the Conference on Argumentation of a comprehensive logic at the service of 1986 (eds. Frans H. van Eemeren, Rob culture in general, a logic with a human face, Grootendorst a.o.), Dordrecht: Foris Publica­ so to speak, may be propagated. tions 1987: 33-45. 18 E. W. Beth, 'Opmerkingen over analytische wijsbegeerte' (Remarks on analytic 10 Unpublished Master's Thesis, University of philosophy), Algemeen Nederlands Tijdschrift Amsterdam, 1988. voor Wijsbegeerte53 (1961), No.5, 1-5. The 11 More historical and technical details are found paper is a critique of the perspective and in another variant of this paper (to be had from classifications of J. O. Urmson who had offered the author on request). distinctions that Beth (rightly, in my opinion) judged to be historically and systematically 12 Beth's sometime student J. F. Staal did research untenable, within the confines of a provincial on Indian logic. 1. F. Staal, 'Contraposition in British outlook on what is to count as analytic Indian Logic', in: Logic, Methodology and philosophy, as described in his Philosophical Philosophy of Science: Proceedings of the 1960 Analysis: its development between the two International Congress, Stanford 1962,634-49; world wars (Oxford, 1956). also 'Negation and the Law of Contradiction in Indian Thought: A Comparative Study', 19 Cf. Beth's reluctance as an organizer to put BuJJetin of the School of Oriental and African logic under general philosophy or under Studies 25 (1962), 52-71. In this connection I mathematics-see Section 5 above. It seems to would like to mention Joseph Wenzel's paper me that Beth's hopes for logic do not thrive at the Venice conference on Wake Forest under the organizational solution that he did University in 1988, which in my opinion reports choose either: a separate association for Logic, on research with high relevance to what Beth Methodology, and Philosophy of Science. meant here. There is very little understanding among its members for his wish to develop a broadly 13 Translated from the Dtitch by E. M. Barth; cf. culturally and politically as well as math­ Beth (1960), Beth (1970) 131 ff. ematically and scientifically oriented logic.

Works by Evert W. Beth

An almost complete bibliography is found in: Amsterdam, The Netherlands. 1. F. Staal, 'E. W. Beth 1908-1964" Dialectica­ The following among his books are of particular International Review of Philosophy of Know/edge 19 (1965), 160-179. A practically complete interest from a general philosophical point of view bibliography can be had from the Evert Willem (and contain further bibliographical data): Beth Foundation, P.O. Box 19121, 1000 GC - The Foundations of Mathematics-A Study in 10 E. M. Barth the Philosophy of Science, Amsterdam: North­ Assen (Holland): Van Gorcum & Compo 1964.) Holland Publishing Company 1959, 1965 (revis­ ed edition). Paper, Harper & Row 1966 (Harper -Aspects of Modern Logic. Dordrecht: D. Reidel Torchbooks, The Science Library, TB 581 X). 1970. (Trans!. by D.H.J. de Jongh and S. de Parts I and IX are of a direct philosophical impor­ Jongh-Kearl from: Moderne logica. Assen: Van tance. Parts II, III, V and VI presuppose that the Gorcum & Compo 1967.) Written for beginners reader already takes a certain inlerest in the pro­ in logic and containing the best introduction to his blems of the foundations of mathematics ("What method of "semantic tableaux". is mathematics about?") or of logic ("Where do logical paradoxes corne from?"). Parts IV, VII and VIII treat of metamathematical problems concer­ E.M. BARTH ning the scope of formalized symbolic systems. INSTITUTE FOR LOGIC, THEORETICAL PHILOSOPHY AND THE HISTORY -' Considerations about Logical Thinking,' OF THE EXACT SCIENCES Mededelingen der Kon Akad. van Wet., N.R., vol. GRONINGEN UNIVERSITY 23, No.1 (1960). Reprinted in (1970). and -Science, A Road to Wisdom. Collected philo­ THE EVERT WILLE.\! BETH FOUNDA TION sophical studies. Dordrecht (Holland): D. Reidel, pia THE ROYAL NETHERLANDS ACADEMY 1968. (Trans!. by Peter Wesly from Door weten­ OF ARTS AND SCIENCES schap tot wijsheid. Verzamelde wijsgerige studies, P.O. BOX 19121, 1000 GC AMSTERDAM

%Teaching ~ Philosophy Teaching Philosophy is a quarterly journal which serves as a forum for the exchange of ideas and information about the teaching and learning of philosophy. Articles, discussions, reports and reviews are published on topics such as: • theoretical issues in the teaching of philosophy • innovative methods and classroom stratagems • experimental and interdisciplinary courses • faculty development and student counseling

1990 Subscriptions: $19.50 individuals; $48 institutions. Add $4 for all subscriptions outside the u.s. Order from the PHILOSOPHY DOCUMENTATION CENTER, Bowling Green State University, Bowling Green, OH 43403-0189 USA. Edited by: Arnold Wilson, UniversityofCincinnati, Cincinnati, OJ[ 45221-0206,